viii CONTENTS
group. 6. Examples and particular cases of convolution of measures.
7. Algebraic properties of convolution. 8. Convolution of a measure and a func-
tion. 9. Examples of convolutions of measures and functions. 10. Convolution
of two functions. 11. Regularization.
Chapter XV
NORMED ALGEBRAS AND SPECTRAL THEORY ........304
1. Normed algebras. 2. Spectrum of an element of a normed algebra. 3. Charac-
ters and spectrum of a commutative Banach algebra. The Gelfand transformation.
4. Banach algebras with involution. Star algebras. 5. Representations of algebras
with involution. 6. Positive linear forms, positive Hilbert forms, and representa-
tions. 7. Traces, bitraces, and Hilbert algebras. 8. Complete Hilbert algebras.
9. The Plancherel-Godement theorem. 10, Representations of algebras of con-
tinuous functions. 11. The spectral theory of Hilbert. 12. Unbounded normal
operators. 13. Extensions of hermitian operators.
References................... . m......444
Index.............................447 set of elements xy with x e A and y e B,